Question

A survey asked subjects how many friends they have and whether this number

is associated with their astrological sign (the 12 symbols of the Zodiac). To

compare the reported number of good friends for those who are (married,

widowed, divorced, separated, never married), an ANOVA table reports F =

0.80.

(a) Specify the null and alternative hypotheses for the ANOVA.

(b) Based on what you know about the F distribution; would you guess that F =

0.80 provides strong evidence against Ho? Explain.

(c) Excel reports a P-value of 0.53. Explain how to interpret it.

Answer 1

Let , population mean number of friends of married, widowed, divorced separated an never married people be

(a) The null hypothesis is :-  

      The alternative hypothesis is : is not true .

(b) Based on the f-statistic value and critical F value we know about the F distribution .

    I guess that F = 0.80 would not provide a strong evidence against H₀ because, to reject H_{0 ,} the observed F value (i.e 0.80) should be greater than the critical F value. Now, Critical F values at any standard levels of significance is way larger than 0.80 .So it has no chance to exceed any critical F value.

(c) P-value of 0.53 means the probabilty that the null hypothesis is true is 0.53 .This is actually a very large P-value resulting the acceptance of the null hypothesis.